Facebook boss Mark Zuckerberg has been called on by a parliamentary committee to give evidence about the use of personal data by Cambridge Analytica.
The consulting firm is accused of harvesting the data of 50 million Facebook users without permission and failing to delete it when told to.
Damian Collins, the chairman of the Commons inquiry into fake news, accused Facebook of "misleading" the committee.
London-based firm Cambridge Analytica denies any wrongdoing.
Both companies are under scrutiny following claims by a whistleblower, Christopher Wylie, who worked with Cambridge Analytica and alleges it amassed large amounts of data through a personality quiz on Facebook called This is Your Digital Life.
He claims that 270,000 people took the quiz, but the data of some 50 million users, mainly in the US, was harvested without their explicit consent via their friend networks.
Mr Wylie says that data was sold to Cambridge Analytica, which then used it to psychologically profile people and deliver pro-Trump material to them, with a view to influencing the outcome of the 2016 presidential election.
In a letter to Mr Zuckerberg, Mr Collins accused Facebook of giving answers "misleading to the Committee" at a previous hearing which asked whether information had been taken without users' consent.
He said it was "now time to hear from a senior Facebook executive with the sufficient authority to give an accurate account of this catastrophic failure of process".
Requesting a response to the letter by 26 March, the MP added: "Given your commitment at the start of the New Year to "fixing" Facebook, I hope that this representative will be you."(BBC)
His intervention comes after the UK's Information Commissioner Elizabeth Denham said she would be applying to court for a warrant to search the offices of Cambridge Analytica.
The firm insists it followed the correct procedures in obtaining and using data, but it was suspended from Facebook last week.
President Donald Trump welcomed any investigation into Cambridge Analytica as "Americans' privacy should be protected", according to a deputy press secretary at the White House.
Facebook shares fell by a further 5% on Tuesday, following a 6.7% drop on Monday, meaning that in total, about $50bn has been wiped from its market value.
The company held an open meeting with its employees on Tuesday to discuss the matter, but the BBC's North America technology reporter Dave Lee said neither Mr Zuckerberg nor his deputy, Sheryl Sandberg, chaired it.
They have not spoken publically since the story about Cambridge Analytics broke last week, he added.
Meanwhile, consumer watchdog the US Federal Trade Commission – which has the power to levy large fines – has reportedly opened an investigation into Facebook.
Undercover filming
Dr Aleksandr Kogan, who created the personality app from which the data had been harvested, is a senior research associate at the University of Cambridge.
A spokesman from the university said they had "sought and received assurances" from Dr Kogan that no University data, resources or facilities were used for his work and they had found no evidence to contradict that.
However, he confirmed the university was writing to Facebook to "request all relevant evidence in their possession".
Meanwhile, Channel 4 News has also broadcast hidden camera footage in which Cambridge Analytica chief executive Alexander Nix appears to suggest tactics his company could use to discredit politicians online